Physics for scientists

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Chapter Physics for Scientists & Engineers, with Modern Physics, 4th edition Giancoli Chapter Introduction, Measurement, Estimating Units of Chapter • The Nature of Science • Models, Theories, & Laws • Measurement & Uncertainty; Significant Figures (reviewed in lab) • Units, Standards, & the SI System • Converting Units • Order of Magnitude: Rapid Estimating • Dimensions and Dimensional Analysis The Scientific Method • Feynman: How not to be fooled… • Observing – Trends, Patterns, Singular Events • Asking Questions – What? When? Where? How? … and WHY? – Researching prior explanations & models • Developing Testable Hypothesis The Scientific Method • Creating Experiments to TEST Hypothesis – There is always uncertainty in every measurement, in every result – Building a model *is* an experiment • Analyzing results – Anticipate sources of error – Refine or Discard Hypothesis – Develop further tests & Repeat! – Compare results w/ existing theories The Scientific Method • Sharing preliminary results – Submit a paper to peer-reviewed journal – Ask colleagues for input – Present at conferences – Discuss, Debate, Defend results • Seeking independent confirmation • Revising Theories • Publishing 1-1 The Nature of Science •Observation: important first step toward scientific theory; requires imagination to tell what is important •Theories: created to explain observations; will make predictions •Further Observations will tell if the prediction is accurate, and the cycle goes on •No theory can be absolutely verified, although a theory can be proven false 1-1 The Nature of Science •How does a new theory get accepted? • Predictions agree better with data • Explains a greater range of phenomena •Example: Aristotle believed that objects would return to a state of rest once put in motion •Galileo realized that an object put in motion would stay in motion until some force stopped it 1-1 The Nature of Science The principles of physics are used in many practical applications, including construction Communication between architects and engineers is essential if disaster is to be avoided 1-2 Models, Theories, and Laws •Models: useful to help understand phenomena • creates mental pictures, but must be careful to also understand limits of model •not take it too seriously •Example: model bay bridge turnbuckle to estimate whether it can withstand load… •A theory is detailed; gives testable predictions •Example: Theory of Damped Harmonic Oscillators 1-3 Measurement and Uncertainty; Significant Figures •Calculators will not give right # of sig figs; usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point) •top image: result of 2.0/3.0 •bottom image: result of 2.5 x 3.2 1-3 Measurement and Uncertainty; Significant Figures Conceptual Example 1-1: Significant figures Using a protractor, you measure an angle to be 30° (a) How many significant figures should you quote in this measurement? (b) Use a calculator to find the cosine of the angle you measured 1-3 Measurement and Uncertainty; Significant Figures Scientific notation is commonly used in physics; it allows the number of significant figures to be clearly shown For example, we cannot tell how many significant figures the number 36,900 has However, if we write 3.69 x 104, we know it has three; if we write 3.690 x 104, it has four Much of physics involves approximations; these can affect the precision of a measurement also 1-3 Accuracy vs Precision Accuracy is how close a measurement comes to the true value ex Acceleration of Earth’s gravity = 9.81 m/sec2 Your experiment produces 10 ± 1m/sec2 You were accurate, but not super “precise” Precision is the repeatability of the measurement using the same instrument ex Your experiment produces 8.334 m/sec2 You were precise, but not very accurate! 1-5 Converting Units Unit conversions involve a conversion factor Example: in = 2.54 cm Equivalent to: = 2.54 cm/in Measured length = 21.5 inches, converted to centimeters? How many sig figs are appropriate here? 1-5 Converting Units Example 1-2: The 8000-m peaks The 14 tallest peaks in the world are referred to as “eightthousanders,” meaning their summits are over 8000 m above sea level What is the elevation, in feet, of an elevation of 8000 m? 1-5 Converting Units • • • • • m = 3.281 feet 8000 m = 2.6248 E04 or 26,248 feet “8000 m” has only significant digit! Round the answer up to 30,000 ft! Rather rough! • 30,000 – 26,248 = 3,752 • 3,752/26,248 = 14.3% high! 1-6 Order of Magnitude: Rapid Estimating Quick way to estimate calculated quantity: - round off all numbers to one significant figure and then calculate - result should be right order of magnitude; expressed by rounding off to nearest power of 10 1-6 Order of Magnitude: Rapid Estimating Example 1-5: Volume of a lake Estimate how much water there is in a particular lake, which is roughly circular, about km across, and you guess it has an average depth of about 10 m 1-6 Order of Magnitude: Rapid Estimating Example 1-6: Thickness of a page Estimate the thickness of a page of your textbook (Hint: you don’t need one of these!) 1-6 Order of Magnitude: Rapid Estimating Example 1-7: Height by triangulation Estimate the height of the building shown by “triangulation,” with the help of a bus-stop pole and a friend (See how useful the diagram is!) 1-7 Dimensions and Dimensional Analysis Dimensions of a quantity are the base units that make it up; they are generally written using square brackets Example: Speed = distance/time Dimensions of speed: [L/T] Quantities that are being added or subtracted must have the same dimensions In addition, a quantity calculated as the solution to a problem should have the correct dimensions 1-7 Dimensions and Dimensional Analysis Dimensional analysis is the checking of dimensions of all quantities in an equation to ensure that those which are added, subtracted, or equated have the same dimensions Example: Is this the correct equation for velocity? Check the dimensions: Wrong! 1-6 Order of Magnitude: Rapid Estimating Example 1-8: Estimating the radius of Earth If you have ever been on the shore of a large lake, you may have noticed that you cannot see the beaches, piers, or rocks at water level across the lake on the opposite shore The lake seems to bulge out between you and the opposite shore—a good clue that the Earth is round 1-6 Order of Magnitude: Rapid Estimating Ex 1-8: Estimating the radius of Earth Climb a stepladder & discover when your eyes are 10 ft (3.0 m) above the water, you can just see the rocks at water level on the opposite shore From a map, you estimate the distance to the opposite shore as d ≈ 6.1 km Use h = 3.0 m to estimate the radius R of the Earth [...]... and Uncertainty; Significant Figures Scientific notation is commonly used in physics; it allows the number of significant figures to be clearly shown For example, we cannot tell how many significant figures the number 36,900 has However, if we write 3.69 x 104, we know it has three; if we write 3.690 x 104, it has four Much of physics involves approximations; these can affect the precision of a measurement...1-2 Models, Theories, and Laws •A law is a brief description of how nature behaves in a broad set of circumstances • Ex: Hooke’s Law for simple harmonic oscillators •A principle is similar to a law, but applies to a narrower range of phenomena •Ex: Principle of Hydrostatic Equilibrium 1-3 Measurement and Uncertainty; Significant Figures... Dimensional analysis is the checking of dimensions of all quantities in an equation to ensure that those which are added, subtracted, or equated have the same dimensions Example: Is this the correct equation for velocity? Check the dimensions: Wrong! 1-6 Order of Magnitude: Rapid Estimating Example 1-8: Estimating the radius of Earth If you have ever been on the shore of a large lake, you may have noticed
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